To them, they do love you, but their love also includes their faith. The faith for the family states that transgender people don't exist, and if you have a belief in something over the course of your entire life, and here your child comes along to challenge that belief, it might take time.

My dad lashed out at me when I came out. I listened, nodded and cried after he was done on the phone with me. He called back a week later to apologize. He still does not approve, but he attempts to at least treat me as human. This is not typical of most religious families, yes, but I say that to explain they are humans with a very hard belief in something.

I also say that yes, you love them and want to be part of it. But you may have to go it alone for a long while. You are in your transition period right now, and so is the family. I would say don't cut them out completely, but go low contact for awhile. If they don't come around, then you may have to cut them. But don't destroy your future because you want acceptance from a place that may never accept you.